Skew managed multi-core optical fiber interconnects

ABSTRACT

The embodiments described herein relate to multi-core optical fiber interconnects which include at least two multi-core optical fibers. The multi-core optical fibers are connected such that the core elements of the first multi-core optical fiber are optically coupled to the core elements of the second multi-core optical fiber thereby forming an array of interconnect core elements extending through the optical fiber interconnect. The multi-core optical fibers are constructed such that cross-talk between adjacent core elements in each multi-core optical fiber are minimized. The multi-core optical fibers are also constructed such that time-delays between the interconnect core elements in the array of interconnect core elements are also minimized.

This application claims the benefit of priority under 35 U.S.C. §119 ofU.S. Provisional Application Ser. No. 62/060,064 filed on Oct. 6, 2014the content of which is relied upon and incorporated herein by referencein its entirety.

BACKGROUND

1. Field

The present specification generally relates to optical fiberinterconnects and, more specifically, to multi-core optical fiberinterconnects with reduced optical signal time delays between coreelements within the transmission interconnects.

2. Technical Background

In recent years optical fiber has become accepted as a viablealternative to traditional materials used for data signal communication.Optical fiber is now widely utilized in a variety of electronic devicesto facilitate the high-speed communication of data signals at highbandwidths. However, as the speed and bandwidth of the electroniccomponents in data communication devices increases, there is acorresponding need to increase the speed of optical interconnects whichcouple such devices. One solution to increase the speed of opticalinterconnects is to increase the fiber density of the opticalinterconnects and thereby realize high fiber count connectors. Anothersolution is to utilize multi-core optical fibers in which a plurality ofcore elements are disposed in a common cladding, thus reducing theoverall bulk of the optical interconnect while increasing the fiberdensity (i.e., the core density).

One drawback of multi-core optical fibers is crosstalk between cores inthe fiber. A requirement of low total crosstalk in interconnects limitsthe density of cores within the multi-core optical fiber, and thus thecapacity scaling, compactness, and cost of the interconnect formed fromthe multi-core optical fiber. As such, crosstalk suppression has been aprimary multi-core optical fiber research. To address crosstalk,trench-assisted homogeneous multi-core optical fibers have been proposedto achieve multi-core optical fibers with high core densities andreduced crosstalk. However, one issue of introducing a trench associatedwith each core is the significant increase in fiber manufacturing cost.To overcome this drawback, heterogeneous multi-core optical fibers havebeen proposed. In these multi-core optical fibers any two adjacent coreshave slightly different effective refractive indexes which preventsphase-matching coupling between the cores, thereby suppressingcrosstalk. However, the different propagating constants between the twocores produces large optical signal time delays between the cores,otherwise referred to as skew. This unwanted skew increases thedifficulty of implementing crosstalk equalizers in a communicationsystem. In addition, this unwanted skew prevents multi-core opticalfibers from being used in communication systems which require minimizedoptical signal time delay between the cores, such as, parallel datatransmission between multiple processors in data center applications.

Accordingly, a need exists for alternative interconnects utilizingmulti-core optical fibers.

SUMMARY

According to one embodiment, a multi-core optical fiber interconnectincludes a transmitting multi-core optical fiber having a length L_(T).The multi-core optical fiber interconnect may also include a firsttransmitting core element C_(T) _(_) ₁ positioned in a first commonouter cladding, the first transmitting core element C_(T) _(_) ₁ havinga group refractive index n_(T) _(_) ₁ ^(g) and an effective refractiveindex n_(effT) _(_) ₁. The transmitting mulit-core optical fiber mayalso include a second transmitting core element C_(T) _(_) ₂ positionedin the first common outer cladding adjacent to the first transmittingcore element C_(T) _(_) ₁, the second transmitting core element C_(T)_(_) ₂ having a group refractive index n_(T) _(_) ₂ ^(g) and aneffective refractive index n_(effT) _(_) ₂, wherein n_(effT) _(_) ₁ andn_(effT) _(_) ₂ are different. The multi-core optical fiber interconnectmay also include a receiving multi-core optical fiber comprising havinga length L_(R). The receiving multi-core optical fiber may have a firstreceiving core element C_(R) _(_) ₁ positioned in a second common outercladding, the first receiving core element C_(R) _(_) ₁ having a grouprefractive index n_(R) _(_) ₁ ^(g) and an effective refractive indexn_(effR) _(_) ₁. The receiving multi-core optical fiber may also includea second receiving core element C_(R) _(_) ₂ positioned in the secondcommon outer cladding adjacent to the first receiving core element C_(R)_(_) ₁, the second receiving core element C_(R) _(_) ₂ having a grouprefractive index n_(R) _(_) ₂ ^(g) and an effective refractive indexn_(effR) _(_) ₂, wherein n_(effR) _(_) ₁ and n_(effR) _(_) ₂ aredifferent. The first transmitting core element C_(T) _(_) ₁ may beoptically coupled to the first receiving core element C_(R) _(_) ₁ andthe second transmitting core element C_(T) _(_) ₂ may be opticallycoupled to the second receiving core element C_(R) _(_) ₂. The lengthL_(T) of the transmitting multi-core optical fiber, the length L_(R) ofthe receiving multi-core optical fiber, and the group refractive indexesof the each of the core elements satisfy the relation (n_(T) _(_) ₁^(g)L_(T)+n_(R) _(_) ₁ ^(g)L_(R))=(n_(T) _(_) ₂ ^(g)L_(T)+n_(R) _(_) ₂^(g)L_(R)).

According to another embodiment, a multi-core optical fiber interconnectincludes a first multi-core optical fiber having a length L_(T). Thefirst multi-core optical fiber may have P core elements C_(T) _(_) _(j)positioned in a first common outer cladding, where j is a positiveinteger from 1 to P, P is greater than 1, and each core element C_(T)_(_) _(j) of the first multi-core optical fiber has a group refractiveindex n_(T) _(_) _(j) ^(g) and an effective refractive index n_(effT)_(_) _(j) which is different than an effective refractive index ofadjacent core elements in the first multi-core optical fiber. Themulti-core optical fiber interconnect may also have a second multi-coreoptical fiber having a length L_(R). The second multi-core optical fibermay have P core elements C_(R) _(_) _(j) positioned in a second commonouter cladding, where j is a positive integer from 1 to P, and each coreelement C_(R) _(_) _(j) of the first multi-core optical fiber has agroup refractive index n_(R) _(_) _(j) ^(g) and an effective refractiveindex n_(effR) _(_) _(j) which is different than an effective refractiveindex of adjacent core elements in the second multi-core optical fiber.The first multi-core optical fiber and the second multi-core opticalfiber may be positioned such that each core element C_(T) _(_) _(j) isoptically coupled to a corresponding core element C_(R) _(_) _(j) toform an array of interconnect core elements. A sum (n_(T) _(_) _(j)^(g)L_(T)+n_(R) _(_) _(j) ^(g)L_(R)) of each interconnect core elementis the same for each interconnect core element in the array ofinterconnect core elements.

Additional features and advantages of the multi-core optical fiberinterconnects described herein will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from that description or recognized by practicing theembodiments described herein, including the detailed description whichfollows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description describe various embodiments and areintended to provide an overview or framework for understanding thenature and character of the claimed subject matter. The accompanyingdrawings are included to provide a further understanding of the variousembodiments, and are incorporated into and constitute a part of thisspecification. The drawings illustrate the various embodiments describedherein, and together with the description serve to explain theprinciples and operations of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically depicts a multi-core optical fiber interconnectaccording to one or more embodiments shown and described herein;

FIG. 2 schematically depicts a cross section of a receiving multi-coreoptical fiber of the multi-core optical fiber interconnect of FIG. 1according to one or more embodiments shown and described herein;

FIG. 3 schematically depicts a cross section of a receiving multi-coreoptical fiber of the multi-core optical fiber interconnect of FIG. 1according to one or more embodiments shown and described herein;

FIG. 4 graphically depicts a refractive index profile of one embodimentof a transmitting multi-core optical fiber;

FIG. 5 graphically depicts a refractive index profile of one embodimentof a receiving multi-core optical fiber for use with the transmittingmulti-core optical fiber of FIG. 4 and in which the relative refractiveindex of each receiving core element is different than the relativerefractive index of the corresponding transmitting core element;

FIG. 6 graphically depicts a refractive index profile of one embodimentof a transmitting multi-core optical fiber;

FIG. 7 graphically depicts a refractive index profile of one embodimentof a receiving multi-core optical fiber for use with the transmittingmulti-core optical fiber of FIG. 6 and in which the diameter of eachreceiving core element is different than a diameter of a correspondingtransmitting core element;

FIG. 8 graphically depicts a refractive index profile of one embodimentof a transmitting multi-core optical fiber;

FIG. 9 graphically depicts a refractive index profile of one embodimentof a receiving multi-core optical fiber for use with the transmittingmulti-core optical fiber of FIG. 8 and in which the refractive indexprofile of each receiving core element is different than a refractiveindex profile of a corresponding transmitting core element;

FIG. 10 graphically depicts the power conversion efficiency (y-axis) asfunction of the effective refractive index n_(eff) between atransmitting core element and a receiving core element in a multi-coreoptical fiber interconnect; and

FIG. 11 graphically depicts a refractive index profile of a core element(transmitting or receiving) which includes a low index trench positionaround the core element.

DETAILED DESCRIPTION

Reference will now be made in detail to embodiments of multi-coreoptical fiber interconnects, examples of which are illustrated in theaccompanying drawings. Whenever possible, the same reference numeralswill be used throughout the drawings to refer to the same or like parts.An embodiment of a multi-core optical fiber interconnect isschematically depicted in FIG. 1. In embodiments, the multi-core opticalfiber interconnect may include a transmitting multi-core optical fiberhaving a length L_(T). The multi-core optical fiber interconnect mayalso include a first transmitting core element C_(T) _(_) ₁ positionedin a first common outer cladding, the first transmitting core elementC_(T) _(_) ₁ having a group refractive index n_(T) _(_) ₁ ^(g) and aneffective refractive index n_(effT) _(_) ₁. The transmitting mulit-coreoptical fiber may also include a second transmitting core element C_(T)_(_) ₂ positioned in the first common outer cladding adjacent to thefirst transmitting core element C_(T) _(_) ₁, the second transmittingcore element C_(T) _(_) ₂ having a group refractive index n_(T) _(_) ₂^(g) and an effective refractive index n_(effT) _(_) ₂, wherein n_(effT)_(_) ₁ and n_(effT) _(_) ₂ are different. The multi-core optical fiberinterconnect may also include a receiving multi-core optical fibercomprising having a length L_(R). The receiving multi-core optical fibermay have a first receiving core element C_(R) _(_) ₁ positioned in asecond common outer cladding, the first receiving core element C_(R)_(_) ₁ having a group refractive index n_(R) _(_) ₁ ^(g) and aneffective refractive index n_(effR) _(_) ₁. The receiving multi-coreoptical fiber may also include a second receiving core element C_(R)_(_) ₂ positioned in the second common outer cladding adjacent to thefirst receiving core element C_(R) _(_) ₁, the second receiving coreelement C_(R) _(_) ₂ having a group refractive index n_(R) _(_) ₂ ^(g)and an effective refractive index n_(effR) _(_) ₂, wherein n_(effR) _(_)₁ and n_(effR) _(_) ₂ are different. The first transmitting core elementC_(T) _(_) ₁ may be optically coupled to the first receiving coreelement C_(R) _(_) ₁ and the second transmitting core element C_(T) _(_)₂ may be optically coupled to the second receiving core element C_(R)_(_) ₂. The length L_(T) of the transmitting multi-core optical fiber,the length L_(R) of the receiving multi-core optical fiber, and thegroup refractive indexes of the each of the core elements satisfy therelation (n_(T) _(_) ₁ ^(g)L_(T)+n_(R) _(_) ₁ ^(g)L_(R))=(n_(T) _(_) ₂^(g)L_(T)+n_(R) _(_) ₂ ^(g)L_(R)). Various embodiments of multi-coreoptical fiber interconnects will be described herein with specificreference to the appended drawings.

The phrase “refractive index profile,” as used herein, refers to therelationship between refractive index or relative refractive index andthe dimensions of the optical fiber or the core element of the opticalfiber.

The phrase “relative refractive index,” as used herein, is defined asΔ(r) %=100×(n(r)²−n_(REF) ²)/2n_(i) ², where n_(i) is an extrema of therefractive index in region i (i.e., the minimum or maximum of therefractive index in region i), unless otherwise specified. The relativerefractive index percent is measured at 1550 nm unless otherwisespecified. The term n_(REF) is the average refractive index of thecommon outer cladding of the multi-core optical fiber, which can becalculated, for example, by taking “N” index measurements (n_(c1),n_(c2), . . . n_(cN)) of the common outer cladding (which, in someembodiments, may be undoped silica), and calculating the averagerefractive index by:

$n_{C} = {\left( {1/N} \right){\sum\limits_{i = 1}^{i = N}\; n_{Ci}}}$

As used herein, the relative refractive index is represented by Δn andits values are given in units of “%,” unless otherwise specified. Incases where the refractive index of a region is less than the referenceindex n_(REF), the relative refractive index is negative and is referredto as having a depressed region or depressed-index, and the minimumrelative refractive index is calculated at the point at which therelative refractive index is most negative, unless otherwise specified.In cases where the refractive index of a region is greater than thereference index n_(REF), the relative index percent is positive and theregion can be said to be raised or to have a positive index.

The group refractive index is defined as the ratio of the vacuumvelocity of light to the group velocity in the medium, which can bewritten as:

${n^{g} = {n + {\omega \frac{n}{\omega}}}},$

where n is the refractive index and ω is the light radian frequency. Thegroup refractive index of an optical fiber is normally measured by usinginterferometric methods, such as the method based on a Fabry-Perotresonator (reported in “Group effective indices of different types ofoptical fibers measured around 1550 nm,” J. Appl. Phys., Vol. 75, No. 6,15 Mar. 1994).

The effective refractive index can be given for a component (e.g., awaveguide) as a measure of the phase velocity of a light beam in thatcomponent, compared to the propagation of light in a vacuum. Theeffective refractive index n_(eff) has the analogous meaning for lightpropagation in a waveguide; the β value (phase constant) of thewaveguide (for some wavelength) is the effective index times the vacuumwave number:

$\beta = {n_{eff}\frac{2\pi}{\lambda}}$

One method to measure effective refractive index is the prism couplingtechnique which is described in “Phase-velocity measurements using prismoutput coupling for single- and few-mode optical fibers” published onOPTICS LETTERS, Vol. 11, No. 2, p. 106, 1986.

The term “α-profile” or “alpha profile” refers to a relative refractiveindex profile of the core elements, expressed in terms of Δ(r) which isin units of “%”, where r is the radius of the core element and whichfollows the equation:

Δ(r)%=Δ(r _(o))(1−[|r−r _(o)|/(r ₁ −r _(o))]^(α)),

where r_(o) is the point at which Δ(r) is maximum, r₁ is the point atwhich Δ(r) % is zero with respect to the common outer cladding, and r isin the range r_(i)≦r≦r_(f), where Δ is defined as above, r_(i) is theinitial point of the α-profile, r_(f) is the final point of theα-profile, and α is an exponent which is a real number. For a profilesegment beginning at the centerline of a core element (i.e., r=0), theα-profile has the simpler form

Δ(r)%=Δ(0)(1−[|r|/(r ₁)]^(α)),

where Δ(0) is the refractive index delta at the centerline of the coreelement. An α of one corresponds to a triangular profile, and an α of 2describes a parabolic profile. When α is greater than 10, the profile ispractically a step-index profile.

Mode field diameter (MFD) is a measure of the spot size or beam width oflight propagating in a single mode fiber. Mode-field diameter isfunction of the source wavelength, fiber core radius and fiberrefractive index profile. MFD is measured using the Peterman II methodwhere

${{MFD} = {2\; w}},{{{and}\mspace{14mu} w^{2}} = {2\frac{\int_{0}^{\infty}{E^{2}r\ {r}}}{{\int_{0}^{\infty}\left( \frac{E}{r} \right)^{2}}\ }r{r}}}$

where E is the electric field distribution in the fiber and r is theradius of the fiber.

The cutoff wavelength is the minimum wavelength at which an opticalfiber will support only one propagating mode. If the operativewavelength is below the cutoff wavelength, multimode operation may takeplace and the introduction of additional sources of dispersion may limita fiber's information carrying capacity. A mathematical definition canbe found in Single Mode Fiber Optics, Jeunhomme, pp. 39 44, MarcelDekker, New York, 1990 wherein the theoretical fiber cutoff is describedas the wavelength at which the mode propagation constant becomes equalto the plane wave propagation constant in the outer cladding. Thistheoretical wavelength is appropriate for an infinitely long, perfectlystraight fiber that has no diameter variations.

The cutoff wavelength may be measured using a transmitted powertechnique such as the technique described in TIA-455-80B entitled“Measurement Cut-off Wavelength of Uncabled Single-mode Fiber ByTransmitted Power.”

The effective area of a fiber is the area of the fiber in which light ispropagated and is defined as:

${A_{eff} = {2\pi \frac{\left( {\int_{0}^{\infty}{E^{2}r\ {r}}} \right)^{2}}{\int_{0}^{\infty}{E^{4}r\ {r}}}}},$

where E is the electric field associated with light propagated in thefiber and r is the radius of the fiber.

All wavelength-dependent optical properties (such as cutoff wavelength,etc.) are reported herein for the wavelength specified.

The term “crosstalk” in a multi-core fiber is a measure of how muchpower leaks from one core to another, adjacent core. The crosstalkdepends on the refractive index profile of the core and the distancebetween adjacent cores. One way to model the crosstalk is to use thecoupled mode theory assuming two perfect (defect-free) identical cores(core 1 and core 2) separated by a distance D. Light is launched intocore 1 with a power P₀. The power transmitted in each of the cores(i.e., P₁ transmitted in core 1 and P₂ transmitted in core 2) changessinusoidally. The power crosstalk from core 1 to core 2 (in dB) can becalculated using the equation:

$X = {{10\; {\log \left( \frac{P_{2}}{P_{0}} \right)}} = {10\; {\log \left( {\frac{\kappa^{2}}{g^{2}}{\sin^{2}({gz})}} \right)}}}$

where z is the propagation distance, κ is the coupling coefficient, Δβis the mismatch in propagation constant between the modes in each of thecores when they are isolated, and g is a parameter depending on κ andΔβ:

$g^{2} = {\kappa^{2} + \left( \frac{\Delta\beta}{2} \right)^{2}}$

The crosstalk depends on the coupling coefficient κ which, in turn, thatdepends on the refractive index of the core and distance between thecores, and Δβ that depends on the difference in refractive index profilebetween the two cores. According to these equations, the once factorwhich can be utilized to reduce the crosstalk is the couplingcoefficient. The coupling coefficient depends on the overlap integral ofelectrical fields of the fundamental modes guided in the adjacent cores.Increasing the distance between the cores reduces the couplingcoefficient but results in a lower packing density of cores in thefiber. Another factor is the mismatch in the propagation constant Δβbetween the two cores. A small mismatch effectively reduces the maximumpower that can be transferred from one core to another core. Therefore aheterogeneous core design (i.e., non-identical cores) can have lowercrosstalk than homogeneous core design (i.e., identical cores).

For a homogeneous multi-core optical fiber, Δβ due to randomperturbations in the fiber can be much stronger than the couplingcoefficients and constant phase can only be maintained in a short lengthof fiber, i.e. the correlation length of the fiber ΔL. For a long lengthof fiber under straight deployment conditions or with a large benddiameter, the crosstalk X is proportional to the fiber length L and theaverage correlation length ΔL:

X=2κ² LΔL

For a heterogeneous multi-core fiber design, the Δβ between the twocores may be designed to be much larger than the Δβ due to randomperturbation. In this case, the crosstalk is proportional to the fiberlength L and inversely proportional to the average correlation lengthΔL:

$X = {\frac{1}{2}\left( \frac{\kappa}{g} \right)^{2}\frac{L}{\Delta \; L}}$

Referring now to FIG. 1, a multi-core optical fiber interconnect 100 isschematically depicted according to one or more embodiments describedherein. The multi-core optical fiber interconnect 100 is utilized tooptically couple the output of an optical transmitter array 200 to anoptical receiver array 300 such that optical signals output from theoptical transmitter array 200 propagate through the multi-core opticalfiber interconnect 100 and are received in the optical receiver array300. The multi-core optical fiber interconnect 100 generally includes atransmitting multi-core optical fiber 102 having a length L_(T) and areceiving multi-core optical fiber 104 having a length L_(R). In theembodiments described herein, the length L_(T) may be the same as ordifferent than the length L_(R). The transmitting multi-core opticalfiber 102 is joined to the receiving multi-core optical fiber 104 with acoupler 106 or by splicing such that the transmitting core elements(FIG. 2) of the transmitting multi-core optical fiber 102 are opticallycoupled to corresponding receiving core elements (FIG. 3) of thereceiving multi-core optical fiber 104, thereby forming an array ofinterconnected core elements extending along the entire length (i.e.,L_(T)+L_(R)) of the multi-core optical fiber interconnect. Accordingly,each interconnected core element of the array of core elements includesa transmitting core element of the transmitting multi-core optical fiberand a receiving core element of the receiving multi-core optical fibersuch that an optical signal introduced into a transmitting core elementpropagates along the length L_(T) of the transmitting multi-core opticalfiber and into the corresponding receiving core element of the receivingmulti-core optical fiber, eventually propagating the entire length ofthe multi-core optical fiber interconnect 100. The coupler 106 utilizedto join the transmitting multi-core optical fiber 102 and the receivingmulti-core optical fiber 104 may be a conventional fiber connector,mechanical splice, or a fusion splice.

Referring now to FIGS. 2 and 3, cross sections of embodiments of thetransmitting multi-core optical fiber 102 and the receiving multi-coreoptical fiber 104 are schematically depicted. Each of the transmittingmulti-core optical fiber 102 and the receiving multi-core optical fiber104 comprise an array of core elements 108 a, 108 b arranged in a commonouter cladding 110 a, 110 b. The arrays of core elements 108 a, 108 bare oriented in the respective common outer claddings 110 a, 110 b suchthat the long axes of the core elements are generally parallel with oneanother.

In the embodiments of multi-core optical fibers depicted in FIGS. 2 and3, the arrays of core elements 108 a, 108 b include rows of coreelements arranged in a rectangular matrix. Each array of core elements108 a, 108 b contains P core elements where P is an integer greater thanor equal to 2. The maximum number of core elements in each array is lessthan or equal to ((D−2)/20)−1, where D is the fiber outer diameter inμm. Accordingly, it should be understood that the array of core elements108 a in the transmitting multi-core optical fiber 102 includes at leasttwo transmitting core elements and the array of core elements 108 b inthe receiving multi-core optical fiber 104 includes at least tworeceiving core elements. It should also be understood that the number ofcore elements in each of the transmitting multi-core optical fiber 102and the receiving multi-core optical fiber 104 is the same such thateach core element in the transmitting multi-core optical fiber 102 iscoupled to a corresponding core element in the receiving multi-coreoptical fiber 104.

In the embodiments of the multi-core optical fiber interconnects 100described herein, the transmitting core elements of the transmittingmulti-core optical fiber 102 are identified as “transmitting coreelement C_(T) _(_) _(j)” where “T” denotes the core element is atransmitting core element and “j” is an integer from 1 to P, indicatinga specific core element in the array of core elements 108 a. Forexample, for a transmitting multi-core optical fiber 102 where P=2(i.e., a transmitting multi-core optical fiber with 2 core elements),the core elements within the transmitting multi-core optical fiber 102are identified as “transmitting core element C_(T) _(_) ₁” and“transmitting core element C_(T) _(_) ₂.”

Similarly, in the embodiments of the multi-core optical fiberinterconnects 100 described herein, the receiving core elements of thereceiving multi-core optical fiber 104 are identified as “receiving coreelement C_(R) _(_) _(j)” where “R” denotes the core element is areceiving core element and “j” is an integer from 1 to P, indicating aspecific core element in the array of core elements 108 b. For example,for a receiving multi-core optical fiber 104 where P=2 (i.e., areceiving multi-core optical fiber with 2 core elements), the coreelements within the receiving multi-core optical fiber 104 areidentified as “receiving core element C_(R) _(_) ₁” and “receiving coreelement C_(R) _(_) ₂.”

The aforementioned identification convention is also utilized toindicate the interconnectivity between the transmitting core elementsC_(T) _(_) _(j) of the transmitting multi-core optical fiber 102 and thereceiving core elements C_(R) _(_) _(j) of the receiving multi-coreoptical fiber 104. Specifically, each transmitting core element C_(T)_(_) _(j) is optically coupled to a corresponding receiving core elementC_(R) _(_) _(j) having the same “j” value. For example, transmittingcore element C_(T) _(_) ₁ is optically coupled to receiving core elementC_(R) _(_) ₁.

While the embodiments of the transmitting multi-core optical fiber 102and the receiving multi-core optical fiber 104 are depicted in FIGS. 2and 3 as containing rectangular arrays 108 a, 108 b of core elements, itshould be understood that other configurations are possible andcontemplated. For example, the core elements may be arranged in astaggered array in which rows of core elements are laterally offset fromone another such that the core elements of adjacent rows are not alignedin a single column. Alternatively, the core elements may be arranged ina series of concentric circles of which increase in diameter from thecenter of each multi-core optical fiber.

In the embodiments described herein, adjacent core elements in each ofthe transmitting multi-core optical fiber 102 and the receivingmulti-core optical fiber 104 are spaced apart by a distance dr measuredfrom the center of one core element to the center of an adjacent coreelement. For example, in FIG. 2, transmitting core element C_(T) _(_) ₁is spaced apart from transmitting core element C_(T) _(_) ₂ by dr.Similarly, transmitting core element C_(T) _(_) ₁ is spaced apart fromtransmitting core element C_(T) _(_) _(j) by dr. In the embodimentsdescribed herein, the distance dr depends on the overall length of themulti-core optical fiber interconnect. For example, when the overalllength of the multi-core optical fiber interconnect is less than about 2km, the distance dr between adjacent core elements is greater than orequal to about 20 μm. However, for lengths greater than about 2 km, thedistance dr between adjacent core elements may be greater than or equalto 25 μm, such as greater than or equal to about 30 μm.

Still referring to FIGS. 2 and 3, the common outer cladding 110 a, 110 bis formed from silica-based glass (SiO₂) with an index of refractionn_(c1). The index of refraction n_(c1) of the common outer cladding isgenerally less than the index of refraction of the core elements in thecorresponding array of core elements 108 a, 108 b. In some embodimentsthe common outer cladding 110 a, 110 b is substantially free fromdopants or contaminants which would alter the index of refraction of thecommon outer cladding 110 a, 110 b including, without limitation,up-dopants (i.e., germanium and the like) and down-dopants (i.e., boron,fluorine and the like). The term “substantially free,” as used herein,means that the common outer cladding 110 a, 110 b does not contain anyconstituent components intentionally added to the glass of the commonouter cladding 110 a, 110 b but may contain impurities or “tramp”contaminants in an amount less than or equal to about 0.1 wt. %. Inother embodiments, the common outer cladding 110 a, 110 b may compriseone or more up-dopants which increase the refractive index of the silicaglass, or one or more down-dopants which decreases the refractive indexof the silica glass, so long as the index of refraction n_(c1) of thecommon outer cladding is less than the index of refraction of the coreelements in the corresponding array of core elements 108 a, 108 b.

The core elements C_(T) _(_) _(j) of the transmitting multi-core opticalfiber 102 each have a radius r_(T) _(_) _(j), a maximum index ofrefraction n_(T) _(_) _(j), a relative refractive index Δ_(T) _(_) _(j)relative to the common outer cladding 110, a group refractive indexn_(T) _(_) _(j) ^(g), an effective refractive index n_(effT) _(_) _(j),and a mode field diameter MFD_(T) _(_) _(j), where the subscript “T”denotes the core element is in the transmitting multi-core optical fiber102 and the subscript “j” is an integer value denoting a specifictransmitting core element within the transmitting multi-core opticalfiber 102. The core elements C_(R) _(_) _(j) of the receiving multi-coreoptical fiber 104 each have a radius r_(R) _(_) _(j), a maximum index ofrefraction n_(R) _(_) _(j), a relative refractive index Δ_(R) _(_) _(j)relative to the common outer cladding 110, a group refractive indexn_(R) _(_) _(j) ^(g), an effective refractive index n_(effR) _(_) _(j),and a mode field diameter MFD_(R) _(_) _(j), where the subscript “R”denotes the core element is in the receiving multi-core optical fiber104 and the subscript “j” is an integer value denoting a specificreceiving core element within the receiving multi-core optical fiber104.

In the embodiments described herein, the core elements C_(T) _(_) _(j)of the transmitting multi-core optical fiber 102 and the core elementsC_(R) _(_) _(j) of the receiving multi-core optical fiber 104 are singlemode core elements.

The core elements C_(T) _(_) _(j) of the transmitting multi-core opticalfiber 102 and the core elements C_(R) _(_) _(j) of the receivingmulti-core optical fiber 104 are generally formed from silica-basedglass. In the embodiments described herein, the silica-based glass ofthe core elements is doped with one or more dopants which increases theindex of refraction of the core elements. For example, the core elementsmay comprise silica-based glass doped with germanium such as when thecore elements comprise silica (SiO₂) glass up-doped with germania(GeO₂). However, it should be understood that dopants other thangermania may be utilized in the core elements, including, withoutlimitation, TiO₂, ZrO₂, Nb₂O₅ and/or Ta₂O₅. Such dopants may beincorporated in the core elements C_(T) _(_) _(j), C_(R) _(_) _(j)either individually or in combination in order to obtain the desiredindex of refraction n_(T) _(_) _(j), n_(R) _(_) _(j) and relativerefractive index Δ_(T) _(_) _(j), Δ_(R) _(_) _(j). In embodiments, thecore elements may comprise from about 3.2 wt. % to about 40 wt. % GeO₂.For example, in some embodiments, the core elements may comprise fromabout 5.0 wt. % to about 16 wt. % GeO₂, more preferably from about 5.5wt. % to about 10.0 wt. % GeO₂, and, most preferably, from about 5.5 wt.% to about 8.0 wt. % GeO₂, which increases the index of refraction n_(T)_(_) _(j), n_(R) _(_) _(j) of the core elements relative to undopedsilica glass. In embodiments, the relative refractive index Δ_(T) _(_)_(j), Δ_(R) _(_) _(j) of the core elements relative to the common outercladding is greater than or equal to 0.2%. For example, in someembodiments, the relative refractive index Δ_(T) _(_) _(j), Δ_(R) _(_)_(j) of the core elements relative to the common outer cladding isgreater than or equal to about 0.2% and less than or equal to about0.5%, preferably greater than or equal to about 0.3% and less than orequal to about 0.4%.

In the embodiments described herein the group refractive index n^(g) ofthe core elements C_(T) _(_) _(j), C_(R) _(_) _(j) is typically greaterthan or equal to about 1.463 at a wavelength of 1550 nm. For example, insome embodiments the group refractive index n^(g) of the core elementsC_(T) _(_) _(j), C_(R) _(_) _(j) is in a range from greater than orequal to 1.463 and less than or equal to 1.479 at 1550 nm.

In the embodiments described herein the effective refractive indexn_(eff) of the core elements C_(T) _(_) _(j), C_(R) _(_) _(j) istypically greater than or equal to about 1.4445 at a wavelength of 1550nm. For example, in some embodiments the effective refractive indexn_(eff) of the core elements C_(T) _(_) _(j), C_(R) _(_) _(j) is in arange from greater than or equal to 1.4445 and less than or equal to1.448 at 1550 nm.

In embodiments, the core elements may have a cutoff wavelength that isless than or equal to about 1550 nm. In some of these embodiments, thecore elements may have a cutoff wavelength that is less than or equal to1310 nm. In embodiments, the core elements may have mode field diametersMFD_(T) _(_) _(j), MFD_(R) _(_) _(j) in a range from greater than orequal to about 6 μm and less than or equal to about 15 μm, preferablyfrom about 8 μm to about 12 μm. In some embodiments, the core elementsmay have effective areas A_(effT) _(_) _(j), A_(effR) _(_) _(j) fromgreater than or equal to about 28 μm² and less than or equal to about180 μm², preferably from greater than or equal to about 55 μm² and lessthan or equal to 150 μm².

In the embodiments described herein, the core elements C_(T) _(_) _(j),C_(R) _(_) _(j) generally have radii r in the range from greater than orequal to about 3 μm to less than or equal to about 35 μm such that thecore elements are single-moded. For example, when the core elementsC_(T) _(_) _(j), C_(R) _(_) _(j) may have radii r in the range fromgreater than or equal to about 3 μm to less than or equal to about 9 μm,more preferably from greater than or equal to about 4 μm to less than orequal to about 6 μm. In some of these embodiments, the core elements maybe single-moded at wavelengths greater than or equal to about 800 nm.

In the embodiments described herein, the core elements C_(T) _(_) _(j),C_(R) _(_) _(j) may have a step-index refractive index profile or agraded-index refractive index profile (also referred to herein as anα-profile). For example, FIG. 4 schematically depicts the refractiveindex profile of a transmitting multi-core optical fiber in which eachof the core elements has a step-index refractive index profile. In otherembodiments, the core elements C_(T) _(_) _(j), C_(R) _(_) _(j) may havea graded index, such as an α-profile, as is graphically depicted in therefractive index profile of FIG. 8 which includes core elements withstep-index refractive index profiles and α-profiles. In embodimentswhere the core elements have α-profiles, an α-value defines the index ofrefraction of the core element as a function of the radius of theelement. In embodiments where the core elements have α-profiles, theα-value of the α-profile may be in a range from about 1.9 to about 2.2.

Referring now to FIGS. 2 and 11, in some embodiments, the core elementsC_(T) _(_) _(j), C_(R) _(_) _(j) may further comprise a low-indexannulus 180 which surrounds the core element. The low-index annulus 180generally has an index of refraction n_(L) and a radial width r′ greaterthan or equal to about 1 μm and less than or equal to about 12 μm,preferably greater than or equal to about 3 μm and less than or equal toabout 6 μm. The index of refraction n_(L) of the low-index annulus 180is such that n_(L)≦n_(c1)≦n_(T) _(_) _(j) and n_(R) _(_) _(j) whichyields a refractive index profile as depicted in FIG. 11. In someembodiments, the low-index annulus 180 may comprise silica glassdown-doped with fluorine. For example, the low-index annulus 180 maycomprise from about 0.36 wt. % to about 3.0 wt. % fluorine, morepreferably from about 0.72 wt. % to about 2.5 wt. % fluorine, and mostpreferably, from about 1.4 wt. % to about 2.0 wt. % fluorine. Forexample, in some embodiments, the relative refractive index Δ_(L) of thelow-index annulus 180 relative to the common outer cladding is less thanor equal to about −0.1%. In some embodiments, the relative refractiveindex percent Δ_(L) of the low-index annulus 180 relative to the commonouter cladding may be greater than or equal to about −0.7%. For example,in some embodiments, the relative refractive index Δ_(L) of thelow-index annulus 180 is greater than or equal to about −0.7% and lessthan or equal to about −0.1%. In some other embodiments, the relativerefractive index Δ_(L) of the low-index annulus 180 is greater than orequal to about −0.5% and less than or equal to about −0.3%. In someembodiments, the low-index annulus may be positioned in direct contactwith the corresponding core element. In other embodiments, the low-indexannulus may be spaced apart from the corresponding core element C_(T)_(_) _(j), C_(R) _(_) _(j) by an offset spacing d. The offset spacing dmay generally be in the range from greater than 0 μm to less than orequal to about 5 μm. In embodiments, the offset spacing d may generallybe in the range from greater than or equal to about 3 μm to less than orequal to about 5 μm. The low-index annuli 180 generally reduce thecrosstalk between adjacent core elements and facilitate spacing adjacentcore elements closer together than adjacent core elements which do nothave low-index annuli without increasing the amount of crosstalk betweenthe adjacent core elements. Accordingly, in some embodiments describedherein, core elements with low-index annuli may be utilized to decreasethe spacing between adjacent core elements.

In the embodiments described herein, the transmitting multi-core opticalfiber 102 and the receiving multi-core optical fiber 104 areheterogeneous multi-core optical fibers in which any two adjacent coreelements have different effective indexes of refraction. Forming themulti-core optical fibers such that adjacent cores have differenteffective indexes of refraction prevents phase-matching coupling betweenthe cores, thereby suppressing crosstalk. More specifically, FIG. 10graphically depicts the coupling efficiency (i.e., the crosstalk) on they-axis as a function of the difference in the effective index ofrefraction between two adjacent core elements (e.g., |n_(effT) _(_)_(j)−n_(effT) _(_) _(j+1)|). As shown in FIG. 10, the couplingefficiency/crosstalk between the two core elements is maximized when thedifference in the effective index of refraction is zero and decreases asthe difference in the effective index of refraction increases.Accordingly, the effective index of refraction of the two adjacent coreelements should be different (e.g., |n_(effT) _(_) _(j)−n_(effT) _(_)_(j+1)|≠0) to reduce the crosstalk between two adjacent core elements.

Considering that the multi-core optical fibers (transmitting andreceiving) described herein each contain at least two core elements perfiber (i.e., P≧2) with the first two core elements being adjacent to oneanother, the first transmitting core element C_(T) _(_) ₁ of thetransmitting multi-core optical fiber has an effective index ofrefraction n_(effT) _(_) ₁ which is different than the effective indexof refraction n_(effT) _(_) ₂ of the second transmitting core elementC_(T) _(_) ₂ in order to mitigate crosstalk between the adjacent coreelements. Similarly, the first receiving core element C_(R) _(_) ₁ ofthe receiving multi-core optical fiber has an effective index ofrefraction n_(effR) _(_) ₁ which is different than the effective indexof refraction n_(effR) _(_) ₂ of the second transmitting core elementC_(R) _(_) ₂ in order to mitigate crosstalk between the adjacent coreelements.

In the embodiments described herein, adjacent core elements are formedsuch that the crosstalk between is minimized. In some embodiments, thecrosstalk between adjacent core elements is less than −30 dB, preferablyless than −35 dB, and even more preferably less than −40 dB. Inembodiments, reduced crosstalk between adjacent core elements may beachieved by forming the core elements such that the difference in theeffective index of refraction of the core elements is greater than orequal to about 0.2×10⁻⁴ in order to reduce crosstalk between the coreelements. For example, in some embodiments, the difference in theeffective index of refraction of the core elements is greater than orequal to about 1.0×10⁻⁴ or even greater than or equal to about 1.0×10⁻³in order to reduce crosstalk between the core elements.

As noted hereinabove, the effective index of refraction of a coreelement is dependent upon several factors, including the relativerefractive index Δ of the core element as determined relative to thecommon outer cladding and the radius r of the core element. Theeffective refractive index of a core element (transmitting or receiving)is also dependent on the refractive index profile of the core element(i.e., whether the core element has a graded-index refractive indexprofile or a step-index profile). These properties of both thetransmitting core elements C_(T) _(_) _(j) and the receiving coreelements C_(R) _(_) _(j) may be varied during manufacture to achieve thedesired effective refractive indexes n_(effT) _(_) _(j) (or n_(effR)_(_) _(j)) and n_(effT) _(_) _(j+1) (n_(effR) _(_) _(j+1)) in order tominimize or mitigate crosstalk between two neighbor core elements in themulti-core optical fiber interconnect.

In the embodiments described herein, the difference in relativerefractive index Δ between two adjacent core elements is greater than orequal to 0.01%, preferably greater than or equal to 0.02% or evengreater than or equal 0.04%. For example, adjacent transmitting coreelements C_(T) _(_) ₁ and C_(T) _(_) ₂ may have relative refractiveindexes of Δ_(T) _(_) ₁ and Δ_(T) _(_) ₂, respectively, and thedifference between Δ_(T) _(_) ₁ and Δ_(T) _(_) ₂ (i.e., |Δ_(T) _(_)₁−Δ_(T) _(_) ₂|) may be greater than or equal to 0.01% in order toreduce the crosstalk between the adjacent core elements. The same holdstrue for adjacent receiving core elements.

While controlling the effective refractive index between two adjacentcore elements is effective for reducing the crosstalk between adjacentcore elements, the difference in the effective refractive index of theadjacent core elements may also introduce a time delay between opticalsignals propagating in each of the core elements. In the embodimentsdescribed herein, the core elements in each of the transmittingmulti-core optical fiber 102 and the receiving multi-core optical fiber104 are formed to not only reduce crosstalk, but to also mitigateoptical signal time delays between adjacent interconnect core elements(i.e., the interconnect core elements formed by optically coupledtransmitting core element C_(T) _(_) _(j) with receiving core elementC_(R) _(_) _(j)) over the length of the multi-core optical fiberinterconnect.

Specifically, the propagating time T_(n) of an optical pulse in thej^(th) core of a multi-core optical fiber interconnect formed from atransmitting multi-core optical fiber and a receiving multi-core opticalfiber can be written as:

T _(n)=(n _(T) _(_) _(j) ^(g) L _(T) +n _(R) _(_) _(j) ^(g) L _(R))/c,

where n_(T) _(_) _(j) ^(g) and n_(R) _(_) _(j) ^(g) are the groupindexes of refraction of the jth core in the transmitting multi-coreoptical fiber and the receiving multi-core optical fiber, respectively,L_(T) is the length of the transmitting multi-core optical fiber, andL_(R) is the length of the receiving core optical fiber, and c is thespeed of light in vacuum.

In order to mitigate the optical signal time delay between opticalpulses in different core elements within the multi-core optical fiberinterconnect, the group index of refraction of the individual coreelements and the length of each of the transmitting multi-core opticalfiber and the receiving multi-core optical fiber should be selected suchthat the sum

(n _(T) _(_) _(j) ^(g) L _(T) +n _(R) _(_) _(j) ^(g) L _(R))

is substantially equal for each pair of optically coupled core elements(i.e., a transmitting core element C_(T) _(_) _(j) optically coupled toa receiving core element C_(R) _(_) _(j)). For example, in embodimentswhere each of the transmitting multi-core optical fiber and thereceiving multi-core optical fiber have two core elements (i.e., P=2),(n_(T) _(_) ₁ ^(g)L_(T)+n_(R) _(_) ₁ ^(g)L_(R))=(n_(T) _(_) ₂^(g)L_(T)+n_(R) _(_) ₂ ^(g)L_(R)).

In some embodiments, the length L_(T) of the transmitting multi-coreoptical fiber is different than the length L_(R) of the receivingmulti-core optical fiber. Furthermore, in the embodiments describedherein, the effective index of refraction n_(eff) of adjacent coreelements (such as adjacent transmitting core elements C_(T) _(_) ₁ andC_(T) _(_) ₂ or adjacent receiving core elements C_(R) _(_) ₁ and C_(R)_(_) ₂) are different in order to minimize crosstalk between adjacentcore elements, as noted above. In addition, each transmitting coreelement C_(T) _(_) _(j) of the transmitting multi-core optical fiber andeach receiving core element C_(R) _(_) _(j) of the receiving multi-coreoptical fiber are formed with group refractive indexes n_(T) _(_) _(j)^(g) and n_(R) _(_) _(j) ^(g) such that, when each transmitting coreelement C_(T) _(_) _(j) is optically coupled to a correspondingreceiving core element C_(R) _(_) _(j) to form an interconnect coreelement of the multi-core optical fiber interconnect, the relationship(n_(T) _(_) _(j) ^(g)L_(T)+n_(R) _(_) _(j) ^(g)L_(R))=(n_(T) _(_) _(j+1)^(g)L_(T)+n_(R) _(_) _(j+1) ^(g)L_(R)) is satisfied and optical signaltime delays amongst the interconnect core elements are minimized ormitigated.

In embodiments, the group refractive index n_(T) _(_) _(j) ^(g) of eachtransmitting core element is different than the group refractive indexn_(R) _(_) _(j) ^(g) of the receiving core element to which thetransmitting core element is coupled. For example, in embodiments wherethe transmitting multi-core optical fiber and the receiving multi-coreoptical fiber each comprise two core elements, the group refractiveindex n_(T) _(_) ₁ ^(g) of the first transmitting core element C_(T)_(_) ₁ is different than the group refractive index n_(R) _(_) ₁ ^(g) ofthe first receiving core element C_(R) _(_) ₁. Similarly, the grouprefractive index n_(T) _(_) ₂ ^(g) of the second transmitting coreelement C_(T) _(_) ₂ is different than the group refractive index n_(R)_(_) ₂ ^(g) of the second receiving core element C_(R) _(_) ₂.

As noted hereinabove, the group refractive index n^(g) of a core element(transmitting or receiving) is dependent on the properties of the coreelement including the refractive index n of the core element and theradius r of the core element. The group refractive index n^(g) of a coreelement (transmitting or receiving) is also dependent on the refractiveindex profile of the core element (i.e., whether the core element has agraded-index refractive index profile or a step-index profile). Theseproperties of both the transmitting core elements C_(T) _(_) _(j) andthe receiving core elements C_(R) _(_) _(j) may be varied duringmanufacture to achieve the desired group refractive indexes n_(T) _(_)_(j) ^(g) and n_(R) _(_) _(j) ^(g) in order to minimize or mitigateoptical signal time delays amongst core elements in the multi-coreoptical fiber interconnect.

In some embodiments described herein, the relative refractive indexesΔ_(T) _(_) _(j) of the transmitting core elements C_(T) _(_) _(j) aredifferent than the relative refractive indexes Δ_(R) _(_) _(j) of thereceiving core elements C_(R) _(_) _(j) to which they are coupled inorder to achieve the desired group refractive indexes n_(T) _(_) _(j)^(g) and n_(R) _(_) _(j) ^(g) and minimize or mitigate optical signaltime delays amongst core elements of the multi-core optical fiberinterconnect. Referring to FIGS. 4 and 5 by way of example, therefractive index profile of a transmitting multi-core optical fiber 102is graphically depicted in FIG. 4 and the refractive index profile of areceiving multi-core optical fiber 104 is schematically depicted in FIG.5. Each of the transmitting multi-core optical fiber 102 and thereceiving multi-core optical fiber 104 contain eight core elements(i.e., P=8) arranged in two rows of four core elements. As shown inFIGS. 4 and 5, the relative refractive index Δ_(T) _(_) _(j) of eachtransmitting core element C_(T) _(_) _(j) in the transmitting multi-coreoptical fiber 102 is different than the relative refractive index Δ_(R)_(_) _(j) of the corresponding receiving core element C_(R) _(_) _(j) inthe receiving multi-core optical fiber 104 to which it is coupled. Forexample, the relative refractive index Δ_(T) _(_) ₂ of transmitting coreelement C_(T) _(_) ₂ in the transmitting multi-core optical fiber 102 isdifferent than the relative refractive index Δ_(R) _(_) ₂ of thecorresponding receiving core element C_(R) _(_) ₂ in the receivingmulti-core optical fiber 104 to which it is coupled. Similarly, therelative refractive index Δ_(T) _(_) ₈ of transmitting core elementC_(T) _(_) ₈ in the transmitting multi-core optical fiber 102 isdifferent than the relative refractive index Δ_(R) _(_) ₈ of thecorresponding receiving core element C_(R) _(_) ₈ in the receivingmulti-core optical fiber 104 to which it is coupled.

In addition, adjacent core elements in each of the transmittingmulti-core optical fiber 102 and the receiving multi-core optical fiber104 have different relative refractive indexes. For example,transmitting core element C_(T) _(_) ₃ of the transmitting multi-coreoptical fiber 102 has a relative refractive index Δ_(T) _(_) ₃ which isdifferent than the relative refractive index Δ_(T) _(_) ₂ oftransmitting core element C_(T) _(_) ₂, the relative refractive indexΔ_(T) _(_) ₄ of transmitting core element C_(T) _(_) ₄, and the relativerefractive index Δ_(T) _(_) ₆ of transmitting core element C_(T) _(_) ₆.Similarly, receiving core element C_(R) _(_) ₃ of the receivingmulti-core optical fiber 104 has a relative refractive index Δ_(R) _(_)₃ which is different than the relative refractive index Δ_(R) _(_) ₂ ofreceiving core element C_(R) _(_) ₂, the relative refractive index Δ_(R)_(_) ₄ of receiving core element C_(R) _(_) ₄, and the relativerefractive index Δ_(R) _(_) ₆ of receiving core element C_(R) _(_) ₆. Inthis embodiment, varying the relative refractive index between adjacentcore elements of both the transmitting multi-core optical fiber 102 andthe receiving multi-core optical fiber 104 reduces the crosstalk betweenadjacent core elements while varying the relative refractive indexbetween the transmitting core elements C_(T) _(_) _(j) of thetransmitting multi-core optical fiber 102 and the correspondingreceiving core elements C_(R) _(_) _(j) of the receiving multi-coreoptical fiber 104 reduces or mitigates optical signal time delaysbetween adjacent interconnect core elements formed by the coupling ofthe transmitting core elements C_(T) _(_) _(j) to the correspondingreceiving core elements C_(R) _(_) _(j).

Considering that the multi-core optical fibers (transmitting andreceiving) described herein each contain at least two core elements perfiber (i.e., P≧2) with the first two core elements being adjacent to oneanother, the first transmitting core element CT_(—1) of the transmittingmulti-core optical fiber has a relative refractive index Δ_(T) _(_) ₁and the first receiving core element C_(R) _(_) ₁ of the receivingmulti-core optical fiber has a relative refractive index Δ_(R) _(_) ₁which is different than the relative refractive index Δ_(T) _(_) ₁ ofthe first transmitting core element C_(T) _(_) ₁ to which it is coupledin order to reduce or mitigate optical signal time delays. Similarly,the second transmitting core element C_(T) _(_) ₂ of the transmittingmulti-core optical fiber has a relative refractive index Δ_(T) _(_) ₂and the second receiving core element C_(R) _(_) ₂ of the receivingmulti-core optical fiber has a relative refractive index Δ_(R) _(_) ₂which is different than the relative refractive index Δ_(T) _(_) ₂ ofthe second transmitting core element C_(T) _(_) ₂ in order to reduce ormitigate optical signal time delays. In addition, Δ_(T) _(_) ₁ of thefirst transmitting core element C_(T) _(_) ₁ is different than Δ_(T)_(_) ₂ of the second transmitting core element C_(T) _(_) ₂ and Δ_(R)_(_) ₁ of the first receiving core element C_(T) _(_) ₂ is differentthan Δ_(R) _(_) ₂ of the second receiving core element C_(R) _(_) ₂ toreduce crosstalk between the adjacent core elements.

Referring to FIGS. 6 and 7, in some embodiments, the radii of the coreelements C_(T) _(_) _(j), C_(R) _(_) _(j) in each of the transmittingmulti-core optical fiber 102 and the receiving multi-core optical fiber104 are different than the radii of adjacent core elements in the fiberto minimize or mitigate crosstalk between adjacent core elements. Forexample, FIG. 6 shows the refractive index profile of a transmittingmulti-core optical fiber 102 which contains eight core elements (i.e.,P=8) arranged in two rows of four core elements. As shown in FIG. 6, theradius of each transmitting core element C_(T) _(_) _(j) in thetransmitting multi-core optical fiber 102 is different than the radiusof an adjacent core element in the transmitting multi-core opticalfiber. For example, transmitting core element C_(T) _(_) ₂ may have aradius r_(T) _(_) ₂ which is less than the radii of the adjacenttransmitting core elements C_(T) _(_) ₁, C_(T) _(_) ₃, and C_(T) _(_) ₇,each of which have radii r_(T) _(_) ₁, r_(T) _(_) ₃, and r_(T) _(_) ₇,respectively.

In the embodiments described herein, the difference in the radius r_(T)_(_) _(j) of adjacent transmitting core elements C_(T) _(_) _(j) (i.e.,|r_(T) _(_) _(j)−r_(T) _(_) _(j+1)|) and the difference in the radiusr_(R) _(_) _(i) of adjacent receiving core elements C_(R) _(_) _(j)(i.e., |r_(R) _(_) _(j)−r_(R) _(_) _(j+1)|) is greater than or equal to0.1 μm or even greater than 0.25 μm. In some embodiments, the differencemay be greater than or equal to 0.5 μm or even greater than 1.0 μm.

In another embodiment, the radii r_(T) _(_) _(j) of the transmittingcore elements C_(T) _(_) _(j) are different than the radii r_(R) _(_)_(j) of the receiving core elements C_(R) _(_) _(j) to which they arecoupled in order to achieve the desired group refractive indexes n_(T)_(_) _(j) ^(g) and n_(R) _(_) _(j) ^(g) and minimize or mitigate opticalsignal time delays amongst core elements of the multi-core optical fiberinterconnect. Referring to FIGS. 6 and 7 by way of example, therefractive index profile of a transmitting multi-core optical fiber 102is graphically depicted in FIG. 6 and the refractive index profile of areceiving multi-core optical fiber 104 is schematically depicted in FIG.7. Each of the transmitting multi-core optical fiber 102 and thereceiving multi-core optical fiber 104 contain eight core elements(i.e., P=8) arranged in two rows of four core elements. As shown inFIGS. 6 and 7, the radius r_(T) _(_) _(j) of each transmitting coreelement C_(T) _(_) _(j) in the transmitting multi-core optical fiber 102is different than the radius r_(R) _(_) _(j) of the correspondingreceiving core element C_(R) _(_) _(j) in the receiving multi-coreoptical fiber 104 to which it is coupled. For example, the radius r_(T)_(_) ₂ of transmitting core element C_(T) _(_) ₂ in the transmittingmulti-core optical fiber 102 is different than the radius r_(R) _(_) ₂of the corresponding receiving core element C_(R) _(_) ₂ in thereceiving multi-core optical fiber 104 to which it is coupled.Similarly, the radius r_(T) _(_) ₈ of transmitting core element C_(T)_(_) ₈ in the transmitting multi-core optical fiber 102 is differentthan the radius r_(R) _(_) ₈ of the corresponding receiving core elementC_(R) _(_) ₈ in the receiving multi-core optical fiber 104 to which itis coupled. In this embodiment, utilizing transmitting core elementsC_(T) _(_) _(j) and corresponding receiving core elements C_(R) _(_)_(j) with different radii reduces or mitigates optical signal timedelays between adjacent interconnect core elements formed by thecoupling of the transmitting core elements C_(T) _(_) _(j) to thecorresponding receiving core elements C_(R) _(_) _(j).

In the embodiments described herein, the difference in the radius r_(T)_(_) _(j) of the transmitting core elements C_(T) _(_) _(j) and theradius r_(R) _(_) _(j) of the corresponding receiving core elementsC_(R) _(_) _(j) (i.e., |r_(T) _(_) _(j)−r_(R) _(_) _(j)|) is greaterthan or equal to 0.1 μm or even greater than 0.25 μm. In someembodiments, the difference in the radius r_(T) _(_) _(j) of thetransmitting core elements C_(T) _(_) _(j) and the radius r_(R) _(_)_(j) of the corresponding receiving core elements C_(R) _(_) _(j) isgreater than or equal to 0.5 μm or even greater than 1.0 μm.

Considering that the multi-core optical fibers (transmitting andreceiving) described herein each contain at least two core elements perfiber (i.e., P≧2) with the first two core elements being adjacent to oneanother, in embodiments, the first transmitting core element C_(T) _(_)₁ of the transmitting multi-core optical fiber may have a radius r_(T)_(_) ₁ and the first receiving core element C_(R) _(_) ₁ of thereceiving multi-core optical fiber may have a radius r_(R) _(_) ₁ whichis different than the radius r_(T) _(_) ₁ of the first transmitting coreelement C_(T) _(_) ₁ to which it is coupled in order to reduce ormitigate optical signal time delays. Similarly, the second transmittingcore element C_(T) _(_) ₂ of the transmitting multi-core optical fiberhas a radius r_(T) _(_) ₂ and the second receiving core element C_(R)_(_) ₂ of the receiving multi-core optical fiber has a radius r_(R) _(_)₂ which is different than the radius r_(T) _(_) ₂ of the secondtransmitting core element C_(T) _(_) ₂ in order to reduce or mitigateoptical signal time delays.

Referring to FIGS. 8 and 9, in some embodiments, the refractive indexprofiles of the core elements C_(T) _(_) _(j), C_(R) _(_) _(j) in eachof the transmitting multi-core optical fiber 102 and the receivingmulti-core optical fiber 104 are different than adjacent core elementsin the fiber to achieve the desired effective refractive indexesn_(effT) _(_) _(j) and n_(effR) _(_) _(j) to minimize or mitigatecrosstalk between adjacent core elements. For example, FIG. 8 shows therefractive index profile of a transmitting multi-core optical fiber 102which contains eight core elements (i.e., P=8) arranged in two rows offour core elements. As shown in FIG. 8, the refractive index profile ofeach transmitting core element C_(T) _(_) _(j) in the transmittingmulti-core optical fiber 102 is different than the refractive indexprofile of an adjacent core element in the transmitting multi-coreoptical fiber. For example, transmitting core element C_(T) _(_) ₂ mayhave a graded-index refractive index profile (such as the α-profiledepicted in FIG. 8) while the adjacent transmitting core elements C_(T)_(_) ₁, C_(T) _(_) ₃, and C_(T) _(_) ₇ have step-index refractive indexprofiles.

In some other embodiments, the refractive index profiles of thetransmitting core elements C_(T) _(_) _(j) are different than therefractive index profiles of the receiving core elements C_(R) _(_) _(j)to which they are coupled in order to achieve the desired grouprefractive indexes n_(T) _(_) _(j) ^(g) and n_(R) _(_) _(j) ^(g) andminimize or mitigate optical signal time delays amongst interconnectcore elements of the multi-core optical fiber interconnect. Referring toFIGS. 8 and 9 by way of example, the refractive index profile of atransmitting multi-core optical fiber 102 is graphically depicted inFIG. 8 and the refractive index profile of a receiving multi-coreoptical fiber 104 is schematically depicted in FIG. 9. Each of thetransmitting multi-core optical fiber 102 and the receiving multi-coreoptical fiber 104 contain eight core elements (i.e., P=8) arranged intwo rows of four core elements. As shown in FIGS. 8 and 9, therefractive index profile of each transmitting core element C_(T) _(_)_(j) in the transmitting multi-core optical fiber 102 is different thanthe refractive index profile of the corresponding receiving core elementC_(R) _(_) _(j) in the receiving multi-core optical fiber 104 to whichit is coupled. For example, transmitting core element C_(T) _(_) ₂ inthe transmitting multi-core optical fiber 102 may have a graded-indexrefractive index profile (such as the α-profile depicted in FIG. 8)while the corresponding receiving core element C_(R) _(_) ₂ in thereceiving multi-core optical fiber 104 to which it is coupled has astep-index refractive index profile as depicted in FIG. 9. Similarly,transmitting core element C_(T) _(_) ₇ in the transmitting multi-coreoptical fiber 102 may have a step-index refractive index profile whilethe corresponding receiving core element C_(R) _(_) ₇ in the receivingmulti-core optical fiber 104 to which it is coupled has a graded-indexrefractive index profile (such as an α-profile) as depicted in FIG. 9.

In addition, adjacent core elements in each of the transmittingmulti-core optical fiber 102 and the receiving multi-core optical fiber104 have different relative refractive indexes. For example,transmitting core element C_(T) _(_) ₃ of the transmitting multi-coreoptical fiber 102 has a relative refractive index Δ_(T) _(_) ₃ which isdifferent than the relative refractive index Δ_(T) _(_) ₂ oftransmitting core element C_(T) _(_) ₂, the relative refractive indexΔ_(T) _(_) ₄ of transmitting core element C_(T) _(_) ₄, and the relativerefractive index Δ_(T) _(_) ₆ of transmitting core element C_(T) _(_) ₆.Similar, receiving core element C_(R) _(_) ₃ of the receiving multi-coreoptical fiber 104 has a relative refractive index Δ_(R) _(_) ₃ which isdifferent than the relative refractive index Δ_(R) _(_) ₂ of receivingcore element C_(R) _(_) ₂, the relative refractive index Δ_(R) _(_) ₄ ofreceiving core element C_(R) _(_) ₄, and the relative refractive indexΔ_(R) _(_) ₆ of receiving core element C_(R) _(_) ₆. In this embodiment,varying the relative refractive index between adjacent core elements ofboth the transmitting multi-core optical fiber 102 and the receivingmulti-core optical fiber 104 reduces the crosstalk between adjacent coreelements while forming the transmitting core elements C_(T) _(_) _(j) ofthe transmitting multi-core optical fiber 102 and the correspondingreceiving core elements C_(R) _(_) _(j) of the receiving multi-coreoptical fiber 104 with different refractive index profiles reduces ormitigates optical signal time delays between adjacent interconnect coreelements formed by the coupling of the transmitting core elements C_(T)_(_) _(j) to the corresponding receiving core elements C_(R) _(_) _(j).

Considering that the multi-core optical fibers (transmitting andreceiving) described herein each contain at least two core elements perfiber (i.e., P≧2) with the first two core elements being adjacent to oneanother, the first transmitting core element C_(T) _(_) ₁ of thetransmitting multi-core optical fiber may have a step-index refractiveindex profile and the first receiving core element C_(R) _(_) ₁ of thereceiving multi-core optical fiber to which it is coupled may have agraded-index refractive index profile in order to reduce or mitigateoptical signal time delays. Similarly, the second transmitting coreelement C_(T) _(_) ₂ of the transmitting multi-core optical fiber mayhave a graded-index refractive index profile and the second receivingcore element C_(R) _(_) ₂ of the receiving multi-core optical fiber towhich it is coupled may have a step-index refractive index profile inorder to reduce or mitigate optical signal time delays. In addition,Δ_(T) _(_) ₁ of the first transmitting core element C_(T) _(_) ₁ isdifferent than Δ_(T) _(_) ₂ of the second transmitting core elementC_(T) _(_) ₂ and Δ_(R) _(_) ₁ of the first receiving core element C_(T)_(_) ₂ is different that Δ_(R) _(_) ₂ of the second receiving coreelement C_(R) _(_) ₂ to reduce crosstalk between the adjacent coreelements.

Based on the foregoing, it should be understood that the grouprefractive index n^(g) of a core element (transmitting or receiving) isdependent on the relative refractive index Δ of the core element, theradius r of the core element or the refractive index profile of the coreelement (i.e., whether the core element has a graded-index refractiveindex profile or a step-index profile) and that these properties of boththe transmitting core elements C_(T) _(_) _(j) and the receiving coreelements C_(R) _(_) _(j) may be varied during manufacture to achieve thedesired group refractive indexes n_(T) _(_) _(j) ^(g) and n_(R) _(_)_(j) ^(g) in order to minimize or mitigate optical signal time delaysamongst core elements in the multi-core optical fiber interconnect. Itshould also be understood that various combinations two or all three ofthese properties may be used to achieve the desired group refractiveindexes n_(T) _(_) _(j) ^(g) and n_(R) _(_) _(j) ^(g) in order tominimize or mitigate optical signal time delays amongst core elements inthe multi-core optical fiber interconnect. For example, combinations ofthe relative refractive index Δ of the core element and the radius r ofthe core element, the relative refractive index Δ of the core elementand the refractive index profile of the core element, the radius r ofthe core element and the refractive index profile of the core element,or the relative refractive index Δ of the core element, the radius r ofthe core element, and the refractive index profile of the core elementmay be used to achieve the desired group refractive indexes n_(T) _(_)_(j) ^(g) and n_(R) _(_) _(j) ^(g) in order to minimize or mitigateoptical signal time delays amongst interconnect core elements in themulti-core optical fiber interconnect.

In addition to the foregoing, the mode field diameters of thetransmitting core optical fibers C_(T) _(_) _(j) of the transmittingmulti-core optical fiber 102 and the receiving core optical fibers C_(R)_(_) _(j) of the receiving multi-core optical fiber 104 should be thesame or substantially the same in order to minimize insertion losses andcrosstalk arising from the coupling of the transmitting multi-coreoptical fiber 102 and the receiving multi-core optical fiber 104. Thatis:

MFD_(T) _(_) _(j)≈MFD_(R) _(_) _(j)

where MFD_(T) _(_) _(j) and MFD_(R) _(_) _(j) are the mode fielddiameters of the j^(th) cores of the transmitting multi-core opticalfiber 102 and the receiving multi-core optical fiber 104. This conditioncan be achieved by selecting the core parameters, such as radius,refractive index, and refractive index profile. In the embodimentsdescribed herein, the difference in the mode field diameter MFD_(T) _(_)_(j) of the transmitting optical fiber core element C_(T) _(_) _(j) andthe mode field diameter MFD_(R) _(_) _(j) of the receiving optical fibercore element C_(R) _(_) _(j) (i.e., |MFD_(T) _(_) _(j)−MFD_(R) _(_)_(j)|) is less than or equal to 1.5 μm, such as less than or equal to1.0 μm or even less than or equal to 0.75 μm.

The multi-core optical fiber interconnects described herein may beformed using techniques similar to those described in U.S. patentapplication Ser. No. 13/273,495 filed Oct. 14, 2011 and entitled“MULTI-CORE OPTICAL FIBER RIBBONS AND METHODS FOR MAKING THE SAME,” theentirety of which is incorporated herein by reference. While theaforementioned patent application describes methods for makingmulti-core optical fiber ribbons, it should be understood that similartechniques may be utilized to produce multi-core optical fibers withdifferent cross-sectional configurations, including, without limitation,multi-core optical fibers which are circular in cross section.

EXAMPLES

The embodiments of multi-core optical fiber interconnects describedherein will be further clarified by the following hypothetical examplesof core elements which may be used for either the transmittingmulti-core optical fiber or the receiving multi-core optical fiber of amulti-core optical fiber interconnect.

Example 1

Table 1 below contains six design examples (D1-D6) of single-moded coreelements which may be used for either the transmitting multi-coreoptical fiber or the receiving multi-core optical fiber of a multi-coreoptical fiber interconnect. Example D1 is similar to a standard singlemode fiber core design. The fiber is single-moded at both 1310 and 1550nm wavelength windows. Example D2 has a higher core delta and smallercore radius than a typical single-moded core element and the mode fielddiameters (MFDs) are smaller than those of standard single-mode opticalfiber core elements. Example D3 has an increased core radius which hasthe effect of increasing the MFDs of the core element. However, thecutoff wavelength of the LP11 mode is higher than 1310 nm so the fiberis single-moded at only the 1550 nm windows. Example D4 has agraded-index refractive index profile with α=2. Examples D5 and D6 havestep-index refractive index profiles which are surrounded by a low-indexannulus in the cladding, helping to reduce both fiber bending losses andcrosstalk between adjacent core elements.

TABLE 1 Core Element Design Examples Example D1 D2 D3 D4 D5 D6 Coredelta (%) 0.34 0.36 0.36 0.4 0.33 0.32 Core radius (μm) 4.3 4.2 4.8 5.65.0 5.1 Alpha 20 20 20 2 20 20 Offset (μm) na na na na 0 1.85 Trenchdelta (%) na na na na −0.1 −0.4 Trench width (μm) na na na na 5 3.1 LP11cutoff wavelength (nm) 1292 1290 1469 1297 1290 1293 LP01 mode fielddiameter at 1310 nm (μm) 9.1 8.8 na 9.1 9.1 9.2 LP01 effective area at1310 nm (μm²) 64.5 60.9 na 62.7 67.9 71.1 LP01 effective index at 1310nm 1.449368 1.449511 na 1.449351 1.449503 1.449472 LP01 group index at1310 nm 1.467218 1.467544 na 1.467174 1.467361 1.467243 LP01 mode fielddiameter at 1550 nm (μm) 10.3 10.0 10.3 10.4 10.0 9.9 LP01 effectivearea at 1550 nm (μm²) 81.2 77.6 83.0 81.5 79.3 80.2 LP01 effective indexat 1550 nm 1.446061 1.446173 1.446603 1.446054 1.446178 1.446150 LP01group index at 1550 nm 1.467848 1.468152 1.468397 1.467757 1.4682011.468237

Example 2

Table 2 below contains six examples of core pairings which may be usedto form interconnect core elements of a multi-core optical fiberinterconnect, specifically referring to the Examples D1-D6 from Table 1above. In these examples, Core I may be a transmitting optical fibercore element CT_j of the transmitting multi-core optical fiber and CoreII may be a receiving optical fiber core element CR_j of the receivingmulti-core optical fiber. Alternatively, Core II may be a transmittingoptical fiber core element CT_j of the transmitting multi-core opticalfiber and Core I may be a receiving optical fiber core element CR_j ofthe receiving multi-core optical fiber. As shown in Table 2, theeffective index difference between the two cores in each pairing isgreater than 0.2×10⁻⁴, which is sufficient to reduce the crosstalkbetween adjacent interconnect core elements. In addition, the spacing drbetween adjacent core elements is greater than or equal to 25 um tofurther mitigate crosstalk between adjacent core elements. The MFDmismatch between coupled cores (i.e., Core I and Core II) is less than0.4 um, which is suitable to mitigate splice and coupling losses.Further, the group index (Table 1) of each core element in a pairing isapproximately the same, meaning that a multi-core optical fiberinterconnect formed from the pairing will have minimal optical signaltime delays amongst adjacent interconnect core elements. This also meansthat the lengths (L_(T) and L_(R)) of the transmitting multi-coreoptical fiber and the receiving multi-core optical fiber forming themulti-core optical fiber interconnect being approximately the same.

TABLE 2 Multi-core optical fiber design example. Effective EffectiveIndex Index MFD MFD Core difference difference difference differencespac- at at at at Core Core ing 1310 nm 1550 nm 1310 nm 1550 nm I II(um) (×10⁻⁴) (×10⁻⁴) (um) (um) 1 D1 D2 50 1.43 1.12 0.3 0.3 2 D1 D3 40na 5.4 na 0 3 D2 D4 45 1.60 1.12 0.3 0.4 4 D1 D5 35 1.35 1.17 0 0.3 5 D2D6 30 0.40 0.23 0.4 0.1 6 D5 D6 25 0.31 0.28 0.1 0.1

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the embodiments describedherein without departing from the spirit and scope of the claimedsubject matter. Thus it is intended that the specification cover themodifications and variations of the various embodiments described hereinprovided such modification and variations come within the scope of theappended claims and their equivalents.

What is claimed is:
 1. A multi-core optical fiber interconnect comprising: a transmitting multi-core optical fiber comprising: a length L_(T); a first transmitting core element C_(T) _(_) ₁ positioned in a first common outer cladding, the first transmitting core element C_(T) _(_) ₁ having a group refractive index n_(T) _(_) ₁ ^(g) and an effective refractive index n_(effT) _(_) ₁; a second transmitting core element C_(T) _(_) ₂ positioned in the first common outer cladding adjacent to the first transmitting core element C_(T) _(_) ₁, the second transmitting core element C_(T) _(_) ₂ having a group refractive index n_(T) _(_) ₂ ^(g) and an effective refractive index n_(effT) _(_) ₂, wherein n_(effT) _(_) ₁ and n_(effT) _(_) ₂ are different; a receiving multi-core optical fiber comprising: a length L_(R); a first receiving core element C_(R) _(_) ₁ positioned in a second common outer cladding, the first receiving core element C_(R) _(_) ₁ having a group refractive index n_(R) _(_) ₁ ^(g) and an effective refractive index n_(effR) _(_) ₁; a second receiving core element C_(R) _(_) ₂ positioned in the second common outer cladding adjacent to the first receiving core element C_(R) _(_) ₂, the second receiving core element C_(R) _(_) ₂ having a group refractive index n_(R) _(_) ₂ ^(g) and an effective refractive index n_(effR) _(_) ₂, wherein n_(effR) _(_) ₁ and n_(effR) _(_) ₂ are different, wherein: the first transmitting core element C_(T) _(_) ₁ is optically coupled to the first receiving core element C_(R) _(_) ₁ and the second transmitting core element C_(T) _(_) ₂ is optically coupled to the second receiving core element C_(R) _(_) ₂; and (n _(T) _(_) ₁ ^(g) L _(T) +n _(R) _(_) ₁ ^(g) L _(R))=(n _(T) _(_) ₂ ^(g) L _(T) +n _(R) _(_) ₂ ^(g) L _(R)).
 2. The multi-core optical fiber interconnect of claim 1, wherein the group refractive index n_(T) _(_) ₁ ^(g) and the group refractive index n_(R) _(_) ₁ ^(g) are different.
 3. The multi-core optical fiber interconnect of claim 2, wherein the group refractive index n_(T) _(_) ₂ ^(g) and the group refractive index n_(R) _(_) ₂ ^(g) are different.
 4. The multi-core optical fiber interconnect of claim 1, wherein: the first transmitting core element C_(T) _(_) ₁ has a relative refractive index Δ_(T) _(_) ₁; the first receiving core element C_(R) _(_) ₁ has a relative refractive index Δ_(R) _(_) ₁ which is different than the relative refractive index Δ_(T) _(_) ₁; the second transmitting core element C_(T) _(_) ₂ has a relative refractive index Δ_(T) _(_) ₂; the second receiving core element C_(R) _(_) ₂ has a relative refractive index Δ_(R) _(_) ₂ which is different than the relative refractive index Δ_(T) _(_) ₂; the relative refractive index Δ_(T) _(_) ₁ of the first transmitting core element C_(T) _(_) ₁ is different than the relative refractive index Δ_(T) _(_) ₂ of the second transmitting core element C_(T) _(_) ₂; and the relative refractive index Δ_(R) _(_) ₁ of the first receiving core element C_(R) _(_) ₁ is different than the relative refractive index Δ_(R) _(_) ₂ of the second receiving core element C_(R) _(_) ₂.
 5. The multi-core optical fiber interconnect of claim 4, wherein: the first transmitting core element C_(T) _(_) ₁ has a radius r_(T) _(_) ₁; the first receiving core element C_(R) _(_) ₁ has a radius r_(R) _(_) ₁ which is different than the radius r_(T) _(_) ₁; the second transmitting core element C_(T) _(_) ₂ has a radius r_(T) _(_) ₂; the second receiving core element C_(R) _(_) ₂ has a radius r_(R) _(_) ₂ which is different than the radius r_(T) _(_) ₂; the radius r_(T) _(_) ₁ of the first transmitting core element C_(T) _(_) ₁ is different than the radius r_(T) _(_) ₂ of the second transmitting core element C_(T) _(_) ₂; and the radius r_(R) _(_) ₁ of the first receiving core element C_(R) _(_) ₁ is different than the radius r_(R) _(_) ₂ of the second receiving core element C_(R) _(_) ₂.
 6. The multi-core optical fiber interconnect of claim 5, wherein: the first transmitting core element C_(T) _(_) ₁ has a step-index refractive index profile; the first receiving core element C_(R) _(_) ₁ has a graded-index refractive index profile; the second transmitting core element C_(T) _(_) ₂ has a graded-index refractive index profile; and the second receiving core element C_(R) _(_) ₂ has a step-index refractive index profile.
 7. The multi-core optical fiber interconnect of claim 4, wherein: the first transmitting core element C_(T) _(_) ₁ has a step-index refractive index profile; the first receiving core element C_(R) _(_) ₁ has a graded-index refractive index profile; the second transmitting core element C_(T) _(_) ₂ has a graded-index refractive index profile; and the second receiving core element C_(R) _(_) ₂ has a step-index refractive index profile.
 8. The multi-core optical fiber interconnect of claim 1, wherein: the first transmitting core element C_(T) _(_) ₁ has a radius r_(T) _(_) ₁; the first receiving core element C_(R) _(_) ₁ has a radius r_(R) _(_) ₁ which is different than the radius r_(T) _(_) ₁; the second transmitting core element C_(T) _(_) ₂ has a radius r_(T) _(_) ₂; the second receiving core element C_(R) _(_) ₂ has a radius r_(R) _(_) ₂ which is different than the radius r_(T) _(_) ₂; the radius r_(T) _(_) ₁ of the first transmitting core element C_(T) _(_) ₁ is different than the radius r_(T) _(_) ₂ of the second transmitting core element C_(T) _(_) ₂; and the radius r_(R) _(_) ₁ of the first receiving core element C_(R) _(_) ₁ is different than the radius r_(R) _(_) ₂ of the second receiving core element C_(R) _(_) ₂.
 9. The multi-core optical fiber interconnect of claim 8, wherein: the first transmitting core element C_(T) _(_) ₁ has a step-index refractive index profile; the first receiving core element C_(R) _(_) ₁ has a graded-index refractive index profile; the second transmitting core element C_(T) _(_) ₂ has a graded-index refractive index profile; and the second receiving core element C_(R) _(_) ₂ has a step-index refractive index profile.
 10. The multi-core optical fiber interconnect of claim 1, wherein: the first transmitting core element C_(T) _(_) ₁ has a step-index refractive index profile; the first receiving core element C_(R) _(_) ₁ has a graded-index refractive index profile; the second transmitting core element C_(T) _(_) ₂ has a graded-index refractive index profile; and the second receiving core element C_(R) _(_) ₂ has a step-index refractive index profile.
 11. The multi-core optical fiber interconnect of claim 1, wherein: the first transmitting core element C_(T) _(_) ₁ has a mode field diameter MFD_(T) _(_) ₁; the first receiving core element C_(R) _(_) ₁ has a mode field diameter MFD_(R) _(_) ₁ which is substantially the same as the mode field diameter MFD_(T) _(_) ₁; the second transmitting core element C_(T) _(_) ₂ has a mode field diameter MFD_(T) _(_) ₂; and the second receiving core element C_(R) _(_) ₂ has a mode field diameter MFD_(R) _(_) ₂ which is substantially the same as the mode field diameter MFD_(T) _(_) ₂.
 12. The multi-core optical fiber interconnect of claim 1 further comprising a low-index trench positioned around at least one of the first transmitting core element C_(T) _(_) ₁, the first receiving core element C_(R) _(_) ₁, the second transmitting core element C_(T) _(_) ₂, and the second receiving core element C_(R) _(_) ₂.
 13. The multi-core optical fiber interconnect of claim 1, wherein the length L_(R) is different than the length L_(T).
 14. A multi-core optical fiber interconnect comprising: a first multi-core optical fiber comprising: a length L_(T); P core elements C_(T) _(_) _(j) positioned in a first common outer cladding, where j is a positive integer from 1 to P, P is greater than 1, and each core element C_(T) _(_) _(j) of the first multi-core optical fiber has a group refractive index n_(T) _(_) _(j) ^(g) and an effective refractive index n_(effT) _(_) _(j) which is different than an effective refractive index of adjacent core elements in the first multi-core optical fiber; a second multi-core optical fiber comprising: a length L_(R); and P receiving core elements C_(R) _(_) _(j) positioned in a second common outer cladding, where j is a positive integer from 1 to P, and each core element C_(R) _(_) _(j) of the first multi-core optical fiber has a group refractive index n_(R) _(_) _(j) ^(g) and an effective refractive index n_(effR) _(_) _(j) which is different than an effective refractive index of adjacent core elements in the second multi-core optical fiber, wherein: the first multi-core optical fiber and the second multi-core optical fiber are positioned such that each core element C_(T) _(_) _(j) is optically coupled to a corresponding core element C_(R) _(_) _(j) to form an array of interconnect core elements; and a sum (n_(T) _(_) _(j) ^(g)L_(T)+n_(R) _(_) _(j) ^(g)L_(R)) of each interconnect core element is the same for each interconnect core element in the array of interconnect core elements.
 15. The multi-core optical fiber interconnect of claim 14, wherein: each core element C_(T) _(_) _(j) has a relative refractive index Δ_(T) _(_) _(j); and each core element C_(R) _(_) _(j) has a relative refractive index Δ_(R) _(_) _(j) which is different than the relative refractive index Δ_(T) _(_) _(j) of a corresponding core element C_(T) _(_) _(j).
 16. The multi-core optical fiber interconnect of claim 14, wherein: each core element C_(T) _(_) _(j) has a radius r_(T) _(_) _(j); and each core element C_(R) _(_) _(j) has a radius r_(R) _(_) _(j) which is different than the radius r_(T) _(_) _(j) of a corresponding core element C_(T) _(_) _(j).
 17. The multi-core optical fiber interconnect of claim 14, wherein each core element C_(T) _(_) _(j) has a different refractive index profile than the corresponding core element C_(R) _(_) _(j).
 18. The multi-core optical fiber interconnect of claim 14, wherein: each core element C_(T) _(_) _(j) has a mode field diameter MFD_(T) _(_) _(j); and each core element C_(R) _(_) ₁ has a mode field diameter MFD_(R) _(_) _(j) which is substantially the same as the mode field diameter MFD_(T) _(_) _(j) of a corresponding core element C_(T) _(_) _(j).
 19. The multi-core optical fiber interconnect of claim 14, wherein P>2.
 20. The multi-core optical fiber interconnect of claim 14, wherein P>4. 